The Responsible Homeowners Act of 2013 would improve upon the government's current Home Affordable Refinance Program (HARP) by eliminating appraisal costs, reducing upfront fees on refinances, ensuring consistent standards for all lenders and providing equal access to refinancing options to all borrowers, the senators said.

The legislation was introduced last year but failed to win Congressional approval.

"We need to bring much-needed relief now to hard-working, responsible homeowners who are struggling to keep up with their high interest-rate loans -- including thousands in New Jersey whom I have heard from," Menendez said in a release. "We need to do this before interest rates go up again. It's time that Congress finally put families first and give homeowners who have played by the rules a fair chance to refinance at today's low rates."

The administration's current HARP program allows borrowers with loans backed by Fannie Mae and Freddie Mac to refinance at lower rates even if they owe more than what their mortgages are worth, so long as they are current on their payments.

The program, which was expanded in October 2011, has helped 1.8 million borrowers and boosted the refinancing business for banks including Wells Fargo (WFC) , JPMorgan Chase (JPM) and U.S. Bancorp (USB) .

But borrowers have still not fully benefited from rock-bottom interest rates because the program currently is structured in a way that limits competition among lenders.

Under HARP, a bank that wants to compete with the current lender for business has to go through tougher underwriting criteria and faces greater risk that Fannie Mae or Freddie Mac would force them to repurchase loans should the borrower default.

As a result, the borrower finds he can often get his loan refinanced only with his current lender and is not able to shop around for a better rate. That allows lenders to charge higher rates.

The senators cited a recent study by Amherst Securities Group that found HARP borrowers are paying more than half a percentage point more than borrowers with other types of loans.

The new bill directs the housing-finance agencies to require the same underwriting standards for new servicers as they do for existing ones, leveling the playing field.

HARP also makes distinctions between borrowers with more equity in their homes and those who are underwater. GSE borrowers who have more than 20% equity in their homes are not eligible for HARP refinancing. The bill seeks to ensure that all GSE borrowers, regardless of the equity in their homes, have the same access to low-cost refinancing options.